1930 on rate has actually been recognized. In fact, Hammett-type correlations are now so generally expected in reactions which involve free radicals that Jaffk’s review of these reactions3 tabulated correlations of rate ratios with a without mentioning that the dimerization of triarylmethyl radicals cannot be correlated in this manner. Evidently the proposal by Walling, Mayo, and cow o r k e r ~that ~ ~ transition states in radical reactions are stabilized substantially by polar effects which involve electron pair delocalization applies quite generally,5l,52 (51) G. A. Russell and R. C. Williamson, Jr., J. Am. Chem. Soc., 86, 2357(1964).
and the rates are correlated better by u+ than by a.53 The structures of the transition states in these reactions are such that delocalization of an unshared electron pair becomes possible (although it would not be possible in the isolated radicals), and this determines substitution behavior in the same manner as in the hydrazyls. It may turn out that only dimerization reactions, in which polar effects cannot be large, will display class S effects of substitution on rates or equilibria. (52) P. D. Bartlett and G. Ruchardt, ibid., 82, 1760 (1960). (53) J. A. Howard and K. U. Ingold, Can. J . Chem., 41, 1744 (1963).
Substituent Effects on the Properties of Stable Aromatic Free Radicals. An LCAO-MO Treatment’ Robert I. Walter Contribution f r o m the Department of Chemistry, Haverford College, Haverford, Pennsylvania 19041. Received June 2, 1965 Abstract: Simple LCAO-MO calculations have been carried out for the I-picryl-2,2-diphenylhydrazyland triphenylmethyl free radicals, and for their derivatives which contain two or three nitro or methoxy groups. Details of the unpaired electron distribution in the hydrazyl radicals are mwe closely reproduced when the parameters used are evaluated systematically. The coulomb integrals are determined from orbital electronegativitiesfor atoms in the correct valence states, corrected for the number of electrons contributed to the A system and for formal charge. Exchange integrals are determined from bond lengths, with the assumption that a bond with a given overlap integral has the same exchange integral as a carbon-carbon bond with the same overlap. The calculations also include a study of the effect of rotation of an aromatic ring on its interaction with two orthogonal 2p atomic orbitals on an adjacent atom which is assumed to be sp hybridized. The results of these calculations reproduce the trends in optical spectra and unpaired electron densities (these must be assumed to be systematically related to the observed nitrogen hyperfine coupling constants) which led to the empirical division of free radicals into two classes, based upon effects of substitution on these properties. The parameters which give the optimum fit of properties of the three hydrazyl radicals are used to predict effects of other types of substitution in this free-radical system. The results show that MO calculations with input parameters whose values lie in a reasonable range can give a wide range of unpaired electron densities on the hydrazine nitrogen atoms, and thus cannot be used to establish the relative values of these densities.
T
his paper presents the results of a theoretical study of the effects of substitution on the optical and esr spectra of two types of stable aromatic free radicals. Experimentally, substitution effects in the l-picryl-2,2diarylhydrazyl and the triarylaminium salt free radicals have been shown to fall into two different patterns. In the former, electron-donor and electron-acceptor substituents in the para positions of the two aromatic rings shift both the nitrogen esr hyperfine coupling constants and the positions of the longest wavelength absorption bands in opposite directions. Free radicals which display this behavior have been labeled class 0. In the triarylaminium salts, both types of substituents shift each of these properties in the same direction. (1) Most of this work was carried out at Columbia University and the University of Minnesota while the author held a National Science Foundation Science Faculty Fellowship in 1960-1961. It is a pleasure to acknowledge the help of Professor Martin Karplus, whose constant interest and generous contributions of advice and background information made it possible to carry out this study. The author is also indebted to the IBM Watson Scientific Laboratory, the Control Data Corporation, and the NASA Institute for Space Studies for donations of computer time. (2) R. I. Walter, J . Am. Chem. SOC.,88, 1923 (1966).
Journal of the American Chemical Society / 88:9 / May 5,1966
Free radicals of this type have been labeled class S. A structural criterion has been proposed for the assignment of other types of aromatic free radicals to the two classes represented by these two series of compounds, and the triarylmethyl radicals fit the assignment to class S on the basis both of their structures and somewhat meager data on their experimental behavior. The additional complications which arise in treating the ionic charge on the aminium salts led to the choice of the triarylmethyl free radicals as representatives of class S in carrying out these computations. No systematic theoretical treatment of substitution effects in these free radicals has been carried out, although calculations have been reported on the unsubstituted compounds. The results of both simple MO and VB computations for triphenylmethyl have been summarized by Karplus and Fraenkel. Comparison with the experimental data shows that there is not a great deal to choose between the quantitative results of the two methods, except in the respect that the VB (3) (a) M. Karplus and G. I
